"Cheeky," she simply captioned a photo of the pair having dinner at the Gold Coast's Moo Moo wine bar and grill. In the pic, 31-year-old Amber is wearing dark red lipstick — and Elon is wearing a dark red kiss print on his cheek.

South African-born Elon is in Australia while Amber films the upcoming action film Aquaman, opposite Jason Momoa, here.

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Before hitting Moo Moo, Amber and Elon made their first public outing as a couple, visiting Currumbin Wildlife Sanctuary where they strolled through the park hand-in-hand and ziplined. They were even joined by two of his sons!

Elon and Amber first met while filming 2013's Machete Kills, in which he had a cameo. The Hollywood Reporter reported that the tycoon soon became "infatuated" with the actress and relentlessly pursued her via email.

"If there is a party or event with Amber, I'd be interested in meeting her just out of curiosity," Musk wrote in an email obtained by The Hollywood Reporter. "Allegedly, she is a fan of George Orwell and Ayn Rand…most unusual," then in a follow-up, "Can you send her a note saying I would like to get together for lunch in LA?"

And in another, "Am not angling for a date. I know she's in a long-term relationship, but … Amber just seems like an interesting person to meet."

Speculation over the duo's relationship has been mounting over the past year. And just last week, Amber's father claimed she was ready to marry Elon.

"Amber and Elon are both very serious about each other," he told Grazia. "She would love to get married. One of the things they want to do is settle down and have a family. They are making plans for that."

Amber finalised her contentious divorce from Johnny Depp in January, while Elon filed for divorce from his actress ex Talulah Riley in January 2015. He has five children from his first marriage to Canadian author Justine Wilson.